Some more thoughts I will post here rather than a PM as others may be following this issue.
I saw where Go Daddy was changing their "Website Builder" from version 6 to version 7 (your pages have v6.2.5) and there was a way through their interface to build pages with their new version 7. I don't know how complex is is to do that or if it is a drag and drop operation. :h That may be a short term solution.
It could be that older templates were based on an older version of PHP code embedded in the templates which the users can not see. I had an issue many years ago where the hosting company was going to upgrade from PHP4 to PHP5 and they told users that any pages written in PHP4 needed to be updated to PHP5 code statements within 6 months. With my VPS boxes I decide which version of code to install and run.
An option for building sites on your own computer are programs like Dreamweaver. You compose the layout, Dreamweaver creates the code and then lets you upload the whole shebang to a normal host.
... still looking for a way to get all your stuff from Go Daddy ...